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When it comes to design, it is usually a good idea to have an idea of design patterns. This will help you better visualize the best way to structure your application. It is worth noting though, that you should choose the design patterns depending on what you need to do, and not try to force your design to conform to a specific design pattern.
At the very ...

No. I would not advice. Android has very specific requirement to the UI to meet the production and of current and future updates on both software and hardware. You can get lazy on the back-end as much as you can get away with.
http://developer.android.com/design/material/index.html

Separation of concerns is just as important in UI as anywhere else, if not more so. Anything that doesn't directly involve user interaction does not belong in the UI. It belongs somewhere else.
Consider what happens when you create a UI having the usual event hooks:
private void Form1_Load(object sender, EventArgs e)
{
listView1.Items.Add(new ...